Fourier curve analyzing and integrating apparatus



N. F. BARNES May 18, 1954 FOURIER CURVE ANALYZING AND INTEGRATINGAPPARATUS 2 Sheets-Sheet 1 Original Filed Sept. 13, 1950 FRgl.

Inventor": Norman FBaPnes,

His Attorney May 18, 1954 N. F. BARNES FOURIER CURVE ANALYZING ANDINTEGRATING APPARATUS 2 Sheets-Sheet 2 Original Filed Sept. 13, 1950Inventor: N or-rnan FIBarnes,

His Attorney.

Patented May 18, 1954 UNITED STATES ATENT OFFICE FOURIER CURVE ANALYZINGAND INTEGRATING APPARATUS New York Original application September 13,1950, Serial No. 184,683. Divided and this application April 7, 1952,Serial No. 280,957

8 Claims.

This application is a division of my Patent 2,602,368 granted July 8,1952, upon an application Serial No. 184,683, filed September 13, 1950,entitled, Color Matching Apparatus, and assigned to the presentassignee. The present application relates to frequency analyzing andintegrated apparatus and more particularly to apparatus providing aFourier integration or analysis of electrical signals in accord withtheir harmonic content. The Fourier curve integrating and analyzingapparatus of the invention is particularly well-suited for matchingcolors through" the medium of their spectrophotometric curves.

In many industrial applications it is often necessary or desirable toanalyze a given electrical function or a given motion or vibrationcharacteristic of a device in terms of harmonically related frequencycomponents. Similarly, it. is often necessary or desirable to integrateor com bine a plurality of harmonically related electrical or mechanicalfrequency components in order to produce a particular desired compositeelectrical curve or mechanical motion characteristic.

The expression Fourier analysis is used herein to connote therepresentation of a composite frequency dependent characteristic interms of its harmonically related frequency com ponents, while theexpression Fourier integration is used herein to connote therepresentation of harmonically related frequency components of acharacteristic in terms of a composite characteristic.

Fourier curve analyzing and integrating apparatus is useful, forexample, in the mixing of 3 color elements such as pigments or dyes, toproduce or match a desired color shade. The spec trophotometrie curvesof the desired color shade and of the color elements may each besubjected to Fourier analysis, and the amounts of each color element tobe used determined on the basis of the amount of each harmonicallyrelated frequency component required to match the correspondingfrequency component disclosed by the Fourier analysis of the desiredcolor shade.

Accordingly, one object of the invention is to provide improved Fourieranalyzing and integrating apparatus.

Another object of the invention is to provide electrical apparatuscapable of instantly delineating a curve representing the Fourierintegral of a series of different-amplitude harmonicallyrelatedfrequency components of a desired characteristic.

Another object of the invention is to provide electrical apparatus whichenables a simple and rapid determination of the amplitude of differentharmonically related frequency components comprising a givenperiodically varying function or curve.

A further specific object of the invention is to provide simpleelectrical apparatus whereby a Fourier analysis of a givenspectrophotometric curve of a color shade or color element may easily beobtained.

In general, the Fourier integrating and analyzing apparatus of theinvention comprises a plurality of commonly driven generatorsconstructed to produce alternating output voltages having harmonicallyrelated frequencies. A voltage of adjustable amplitude and phase isderived from the output circuit of each generator and theseadjustable-amplitude voltages of harmonically related frequencies aresupplied in series with a common impedance element. The voltagedeveloped across this common impedance element represents the Fourierintegral of the individual harmonically related generated volt-' agesand is preferably supplied to the signal receiving terminals of anoscilloscope. The output voltage of the lowest frequency generator ispreferably employed to synchronize the sweep circuit of theoscilloscope. The Fourier integral curve is thus delineated upon theoscilloscope screen.

The novel features which I believe to be characteristic of my inventionare set forth with particularity in the appended claims. My inventionitself, however, together with further objects and advantages thereofcan best be understood by reference to the following description takenin connection with the accompanying drawings in which Fig. 1 is aperspective diagrammatic view of apparatus embodying my invention, Fig.2 is a circuit diagram showing various details of the frequencyanalyzing and integrating apparatus illustrated in Fig. 1 together withmeans for call bra-ting various electric elements employed in thisfrequency generating network, and Fig. 3 is a diagrammatic viewillustrating an alternative construction of the frequency analyzing andintegrating apparatus of Fig. 1. In the drawings similar referencenumerals indicate similar circuit elements.

Referring to Fig. 1, I have shown my invention in one form as embodiedin a color matching apparatus comprising a source 1 of substantiallywhite light which is focused by a lens 2 through an upper slot 3 in alight confining member l upon a spectrum producing means 5 which mayconveniently comprise a concave surface diffraction grating 6 with alight reflecting face as illustrated. The diffraction grating 6functions to separate the white light into a plurality of acent beams ofmonochromatic light While the concave mirrored surface of the grating 6simultaneously reflects and focuses these reflected beams in thedirection of a lower slot 1 in the light confining member 4. Aconventional prism with a light reflecting rear face may, of course, besubstituted for the diffraction grating but additional focusing meansmust then be employed.

The diffraction grating 6 is arranged to be rocked on a shaft 3 by anarm 9 which rides against a cam I under the tension of a spring II. Whenthe grating is rocked, the reflected monochromatic light of the variouswave lengths in the visible spectrum pass over the lower slot 1 and aresuccessively transmitted therethrough. The light transmitted throughslot 1 is focused by a lens I2 through a light receiving aperture I3 ofa light integrating compartment I4. A window I5 of this lightintegrating compartment I4 is constructed to he covered by a sample I6of the color shade to be matched. This sample I6 is aligned so that itreflects the light passing into the compartment I4 through the apertureI3 upon a photoelectric element I1, preferably located within thecompartment I4. For transparent materials the sample may alternativelybe placed in the optical beam between slot 1 and lens I2.

The output voltage produced by the photoelectric device I1, which isresponsive to the intensity of the successive monochromatic light beamsreflected from the sample I5, is amplified by an amplifier I8 and isapplied between a pair of vertical deflection plates I 9 and of acathode ray electric discharge device 2t through a switch 22. Acontacting arm 23 of the switch 22 is constructed to move against thetension of a spring 24 between two contacting positions by the 1'0-tation of a cam 25. During one half cycle of rotation of cam 25, arm 23is held against a contact 26 and the circuit is completed from theoutput of the amplifier I8 to the deflection plates I9 and 20. Duringthe alternate half cycle of the rotation of cam 25, the output circuitof amplifier I S is broken and the arm 23 is held against an oppositecontact 21 to complete the output circuit from Fourier curve integratingand analyzing apparatus designated generally by the numeral 35 andcomprising the present invention. The cams I 8 and are rotated on thesame shaft 28 driven by a motor 29 and their rotational positions on theshaft 28 are relatively adjusted so that the output circuit of theamplifier I8 is completed during the period of one scanning sweep of thespectrum across slot 1.

Also attached to the shaft 28 is a movable arm 33 of a dual-sidedpotentiometer 39, each side being respectively connected across a sourceof voltage designated as battery 3I. The movable arm 30' of thepotentiometer 30 is connected to one horizontal deflection plate 32 ofthe cathode ray discharge device 2I while the other horizontaldeflection plate 33 is connected to a variable tap 34 of the battery 3I. The rotational position of the movable arm 30' of the dualpotentiometer 36 is adjusted with relation to the shaft 28 so that twosuccessive and substantially identical saw-tooth sweep voltages areapplied between the horizontal deflection plates Whose periods coincidewith the alternate contact engaging periods of switch 22 and theback-and-forth scanning periods of the diffraction grating 6. Coincidentwith one sweep voltage the entire spectrum passes across slot 1, theswitch 22 completes the output circuit of the amplifier I8, and theelectric signals representing the spectrophotometric curve of the colorshade of sample I6 are applied to the vertical deflection plates I9, 20to produce a delineation of the spectrophotometric curve of the colorsample I6 on the screen of the cathode ray discharge device 2!.Coincident with the next sweep voltage, the diffraction grating 6returns to its initial position, the output circuit of the amplifier I8is disconnected by switch 22 and the output voltage function of theFourier curve analyzing apparatus 35, is connected to the verticaldeflection plates of the discharge device 2| to delineate a second curveupon the screen of the discharge device 2|. In order to separate the twocurves upon the screen if desired, a biasing voltage, such as may beprovided by a battery 36, is superimposed upon the output voltage of theamplifier I8.

The Fourier curve integrator and analyzer 35 includes a plurality ofalternating current generators 31, 38, 39 and 40 all energized by therotation of a common shaft M and producing alternating currents inassociated output circuits whose frequencies are harmonicallyinterrelated. One of the generators, such as generator 31, may have twopoles while the remaining generators are four-poled, six-poled andeightpoled respectively in order to produce output voltages offrequencies corresponding to a fundamental frequency and its second,third and fourth harmonics. Additional generators having an increasingnumber of poles may be driven by shaft 4| to produce output voltages ofeven higher harmonic frequencies, if desired.

A separate bank of impedances are connected in parallel across theoutput terminals of each of the generators. Impedances designated by thenumerals 42 and 43 are connected in parallel across the output terminalsof the two-poled generator 31, while the impedance designated by thenumerals 44 and 45, 46 and 41, and 48 and 49, are respectively connectedin a similar manner across the output terminals of the four-poledgenerator 38, the six-poled generator 39 and the eight-poled generator40. Although I have shown only two impedances in each bank associatedwith a particular generator, it will be appreciated that many moreparallel impedances may be employed depending upon the number of colorelements to be used in matching the desired color shade.

Each of the impedances in each bank of impedances is connected insequential tandem relation with an associated impedance in each of theother banks of impedances in order to produce a voltage functioncomposed of harmonically related frequency components which representsthe spectrophotometric curve of a particular color element. One group ofimpedances, such as impedances 43, 45, 41 and 49, are interconnected toprovide a voltage function representing the spectrophotometric curve ofone color element; While another group of impedances, such as impedances42, 44, 46 and 48 are interconnected in a similar manner providinga voltage function representing the spectrophotometric curve of a differentcolor element. Each of these impedances 42 through 49 has a fixed centertap and an adjustable tap. The center tap of one impedance in one of thegroups, such as impedance 49, is directly connected to the groundeddeflection plate it while. the. adjustable tap of thisv impedance 49 isconnected t the center tap of impedance 41. Similarly;v the adjustabletap of impedance 4'! is connected to. the fixed center tap of impedance45, and. the adjustable tap of impedance 4.5 is connected to the fixedtap of impedance t3. The movable, tap of impedance 43 is connected toone side of a voltage dividing potentiometer 50 Whose other side isconnected back to the grounded, center tap of impedance dc to provide aclosed series or closed loop circuit. It will thus be seen that thevoltage developed between the fixed center tap and the adjustable tap ofeach impedance in this group is. connected in series circuit relationwith. the potentiometer 5t, and a voltagefunction appears across thispotentiometer 50 which is, the algebraic sum of the harmonicallyinterrelated voltages derived from these individual imp dances. Themagnitude as well as the phase (either positive or negative) of anyharmonic frequency component in this voltage function can then be easilyadjusted by merely varying the position of the adjustable tap of theimpedance element associated with the generator of that particularfrequency voltage.

The movable arm 5| of the potentiometer 50, at which a voltageproportional to this voltage function is produced, is connected: to thecenter tap of one of the impedances, such as impedance 88 in the secondgroup of impedances employed to produce a curve representing thespectrophotometric curve of a different color element. This second groupof impedances designated by numerals 42, 4t, 4t and 48 istheninterconnected in series circuit relation with a secondpotentiometer 52 in the same manner that the first group of impedancesare connected in. series. relaticn with the potentiometer 50. A movablearm 53 of this second potentiometer 52 is then directly connected to thecontact 2.! of the switch 22. When the arm 23 of switch 22 engagescontact 21 the algebraic sum of the voltage function ap peering at themovable arm 5! of potentiometer 5t and the voltage function appearing atthe movable arm 53 of potentiometer 52 is applied across the verticaldeflection plates [9 and 2,0. of the discharge device H. The. relativemagnitude of these voltage functions may be. adjusted by merely varyingthe movable arms. 5! and 53 of the potentiometers 5!! and 52respectively.

In order to synchronize the period of these harmonioally interrelatedvoltage functions to the saw-tooth, sweep voltage applied to the.horizontal deflection plates 32', 3.3, the common shaft ll is preferablydriven, through such means as gears 62, by the shaft 23 upon whichv themovable arm til of the sweep voltage producing dual potentiometer so ismounted. The gear ratio, is preferably 1:1 although other integral gearratios may be employed. Alternatively, the shafts 4| and 26 may beseparately driven bysynchronous motors.

jacent the center of its range, and a sample, of

one of the color elements to be, usedv to obtain. a desired color shadeis placed over the. window 15 of the light integrating compartment. it.or

1!: the: sample is transparent, in the optical beam between slot 1 andlens I2. The motor 29 is turned on and two curves are delineated uponthe screen of the discharge device; one curve representing thespectrophotometric curve of the sample color element and the other curverepresenting the voltage function produced by the harmonicallyinterrelated voltages developed across the first roup of impedances 53,45, 41

and 49. The harmonic content of this voltage function is then adjustedby varying the movable taps of these impedances until the curve producedby the output of the Fourier integrating and analyzing network 35assumes the same configuration as the spectrophotometric curve of thesample color element. The voltage function apnearin across potentiometer58 now represents the spectrophotometric curve of this first colorelement.

This first sample color element is then replaced by a second colorelement to be used in matching the desired color shade, and the movablearm 53 of potentiometer 52 is adjusted to the center of its range, whilethe movable arm 5| of the potentiometer 50 is adjusted to its groundedposition. The curve matching procedure outlined above is then repeatedusing the second group of impedance elements 152, 44, 46 and 48 insteadof the first group of impedances 43, 45, 4! and 49, which are maintainedunaltered in their previously calibrated positions.

After the spectrophotometric curve of this second color element ismatched by the adjustment of this second group of impedances, or of asmany more groups as may be needed, the second sample color element isreplaced by a sample of the color shade to be matched. The relativepositions of the movable arms 5! and 53 of potentiometers 56 and 52respectively are then adjusted until the curve produced by the Fouriernetwork 35 matches the spectrophotometric,

curve of the sample color shade. Since the position of the movable armof each potentiometer 58 and 52 represents the intensity of thespectrophotometric curve of a particular color element, the relativepositions of the movable arm 5| and 53 may be calibrated to indicate therelative amounts of a particular color element that is necessary tomatch the sample color shade.

It is evident that the color matching apparatus illustrated in Fig. 1may also be employed to give a rapid Fourier curve analysis of a samplecolor shade. In this application only one group of impedances, such asimpedances 42, t l, it and 48 need be employed. The movable arm 5! ofimpedance 55 is turned to its grounded position, a sample of the colorshade to be matched is placed over window l5 of light compartment i l;and with movable arm 53 of potentiometer 52 adjusted somewhere adjacentits central position, the adjustable taps of this group of impedances(42, M, 46 and 48) are varied until the two curves which are delineatedupon the screen of the. discharge device 2! assume the sameconfiguration. The relative positions of the adjustable taps of theseimpedances then represent the relative amounts of fundamental andharmonic frequencies which comprise the spectrophotometric curve of thesample color shade.

Referring now to 2, I have shown an. alternative means of calibratingeach group of impedances in the Fourier curve integrating and analyzingnetwork 35 when the spectrophotometric curve. of a particular colorelement is already; known- Only one group. oi impedances (43, 45, 41 and49) are shown in Fig. 2 and are connected in series circuit relationwith potentiometer 50 in a manner similar to Fig. 1. The voltagedeveloped between the movable arm and the grounded end of potentiometer50 is connected to the vertical deflection plates of an externaloscilloscope 54 and the sweep circuit of the oscilloscope issynchronized to the fundamental frequency voltage of the Fourier networkby a connection to the output circuit of the twopoled generator, asindicated. The adjustable taps of impedances 43, 45, 4! and 49 may thenbe varied until the configuration of the curve delineated upon theoscilloscope matches the configuration of the known spectrophotometriccurve of the particular color element concerned.

Referring now to Fig. 3, I have shown in diagrammatic form analternative construction of the harmonic frequency generators togetherwit an alternative Fourier curve integrating and analyzing network. Inorder to simplify the drawing, only one group of impedances isillustrated in conjunction with these harmonic frequency generators. Inthis Fourier curve integrating and analyzing circuit a unidirectionalcurrent is maintained through an inductance 55 associated with each ofthe generators by a parallel connection across a source of voltage, suchas battery 55. The generators each have a rotating cam-like magneticalypermeable member driven by a common shaft which functions to vary thereluctance of its associated inductance 55 at harmonicaly interrelatedfrequen cies. One cam-like member 5'1, which produces the fundamentalfrequency may comprise an eccentrically mounted substantially circularplate which passes close to its associated. inductance once eachrevolution. The remaining cam-like members 58, 58 and 60 have 2, 3 and 4symmetrically disposed extensions respectively, and therefore vary thereluctance of their associated coils at twice, three times and fourtimes the fundamental frequency respectively. Capacitors 6! areconnected in series with the output voltage produced by each impedancein order to transmit only the alternating current component of thevoltage produced across these impedances. The remainder of the circuitis identical to that of Fig. l.

The various alternating voltage generators of Figs. 1, 2, and 3 arepreferably made of individually and adjustably connectable to driveshaft 4| at any desired angular position. In this way the output sinewave voltage from each harmonic frequency generator may be synchronizedin phase with the output voltage from the fundamental frequencygenerator so as to produce zero output voltage at the same instant oftime, or may be displaced in phase relative to the fundamental frequencygenerator output voltage by a determinable phase angle so as to producezero output voltage at an earlier or later instant of time. Such phasedisplacement may be necessary to permit the Fourier integration oranalysis of certain curves that cannot be adequately represented by acombination of phase synchronized harmonically related sinusoidalvoltages.

Although I have shown particular embodiments of my invention, manymodifications may be made and I intend, therefore, by the appendedclaims to cover all such modifications as fall within the true spiritand scope of my invention.

What I claim as new and desire to secure by Letters Patent of the UnitedStates is:

1. Fourier curve integrating and analyzing ap- 'p'aratus comprising aplurality of electric generators constructed to produce output voltagesof harmonicaliy related frequencies, at least one impedance connected inan output circuit of each generator, each impedance having a referencetap and an adjustable tap, the adjustable tap of each impedance beingconnected in sequence to the reference tap of a successive one of saidimpedances to form a closed loop circuit, and a load impedance connectedin series circuit relation with one of said last mentioned connections.

2. A Fourier curve integrating and analyzing network comprising aplurality of electric generators constructed to produce output voltagesof harmonically related frequencies, at least one impedance connected inan output circuit of each generator, each impedance having 9. referencetap and an adjustable tap, the adjustable tap of each impedance beingconnected in sequence to the reference tap of a successive one of saidimpedances to form a closed loop circuit, a load impedance connected insaid closed loop circuit, and means operating synchronously with theperiod of one of said harmonic frequency voltages and controlled by thevoltage developed across said load impedance for producing a curverepresenting the integration of the voltages produced between thereference tap and adjustable tap of each impedance.

3. A Fourier curve integrating and analyzing network comprising aplurality of electric generators, each said generators being driven by acommon motivating force and producing output voltages of harmonicallyrelated frequencies, at least one impedance connected in an outputcircuit of each generator, each impedance having a reference tap and anadjustable tap, the adjustable tap of each impedance being connected insequence to the reference tap of a. successive one of said impedances toform a closed loop circuit, a load impedance connected in said loopcircuit and a cathode ray discharge device having a screen and raydeflecting means for producing a visible trace upon said screen, saidray deflecting means being connected to receive the voltage developedacross said load impedance and delineating a trace upon said screenwhich varies in response thereto.

4. Fourier curve integrating and analyzing apparatus comprising aplurality of electric generators, arranged to be driven by a commonmotivating force and producing output voltages of harmoniously relatedfrequencies, an impedance connected in an output circuit of eachgenerator, each impedance having a reference tap and an'adjustable tap,the adjustable tap of each impedance being connected in sequence to thereference tap of a successive one of said impedances to form a closedseries circuit, a load impedance connected in said closed seriescircuit, and an oscilloscope having deflection plates connected toreceive voltage developed across said load impedance and having a sweepsynchronizing circuit connected to receive the output voltage of one ofsaid generators.

5. Fourier curve integrating and analyzing apparatus comprising aplurality of electric generators constructed to produce output voltagesof harmonically related frequencies, an output circuit for eachgenerator, each output circuit comprising a bank of parallel connectedimpedances, each impedance having an adjustable tap and a reference tap,the adjustable tap of each impedance ofeach bank being connected insequence to a reference tap of a corresponding impedance of each otherbank to form a plurality of closed loop circuits, an independent loadimpedance connected in each loop circuit, and electric utilization meansconnected to re ceive the sum of the voltages developed across said loadimpedances.

6. A Fourier curve integrating and analyzing network comprising aplurality of alternating voltage generators having harmonically relatednumbers of magnetic poles to produce output voltages of harmonicallyrelated frequencies, at least one impedance connected in an outputcircuit of each generator, each impedance having a reference tap and anadjustable tap, the adjustable tap of each impedance being connected insequence to the reference tap of a successive one of said impedances toform a closed loop circuit, and a load impedance connected in seriescircuit relation with one of said last mentioned connections.

'7. A Fourier curve integrating and analyzing network comprising aplurality of variable reluctance devices, means for varying thereluctance of said devices at harmonically related frequenoies, avoltage source, a plurality of impedances, each impedance beingconnected in series with said voltage source and a respective one ofsaid reluctance devices, each impedance having a reference tap and anadjustable tap, the adjustable tap of each impedance being connected insequence to the reference tap of a successive one of said impedances toform a closed loop circuit, and a load impedance connected in saidclosed loop circuit.

8. Fourier curve integrating and analyzing apparatus comprising voltagegenerating means for providing a plurality of independent alternatingvoltages of harmonically related frequencies, means for deriving avoltage of adjustable amplitude and phase from each harmonically relatedalternating voltage, means indicating the amplitude and phase of saidderived voltages, and voltage responsive curve delineating meansconnected to receive the sum of said derived voltages.

Name Date Barnes July 8, 1952 Number

